2008 iTest Problems/Problem 4

Problem

The difference between two prime numbers is $11$ . Find their sum.

Solution

We know that any prime number, excluding $2$ , is congruent to $1 \pmod 2$ . Thus, if both of the primes are not $2$ , their difference would be congruent to $0 \pmod 2$ . Because $11 \equiv 1 \pmod 2$ , one of the primes must be $2$ . It follows that the other prime must then be $13$ . Therefore, the sum of the two is $13+2=\boxed{15}$ .

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2008 iTest Problems/Problem 4

Problem

Solution